At this point we are left occupied with showing (REF )-(REF ).
Condition (REF ) follows from [1]} and (REF ) from [1]}.
The probabilities with which these two conditions hold are revisited in sec:unionbound.
In the following two sections we develop proofs for the remaining three conditions: the coherence between pairs of linear operators (REF ) is shown in sec:coherencepairs and the two dual certificate conditions (REF ) and (REF ) are shown in sec:dualcertificate.
Finally, sec:unionbound synthesizes the probabilities to fulfill each of the five conditions.
